A tunnel must be made through a hill. As a result, a surveyor and an engineer create a sketch of the area. The sketch, displayed below, includes information they have either researched or measured. They need to build a tunnel from the point E to the point H on the sketch. a) Prove the three triangles ΔSFH, ΔEGL, and ΔSIL are similar. b) Use similar triangles to determine the length from H to E.

a) Look step by step explanation

b) x = 498,22

Step-by-step explanation:

a) Two triangles are similar if all their angles are equal

Then in Δ SFH  and  Δ GEL we got:

∡ SFH = ∡ EGL   right angles

∡ LEG = ∡ HSF   since the same straight line (SL) is cut by parallel lines (vertical  segments  EG and SF )

∡ SHF = ∡ ELG  The same straight line SL is cut by two parallel segments FH and GL  ( horizontal segments)

The Δ SIL is similar to the two previous Δs according to:

∡ SIL is a right angle

∡ ILS = ∡ GLE = ∡ FHS

∡ ISL = ∡FSH = ∡GEL

The condition for similar triangles is satisfied

b)

From Δs    FSH and  GEL

SF/EG  = 380/EL

225/180  =  380/EL

225*EL  =  180*380

EL = 180*380/225

EL = 304

From Δs  SIL and SFH

225/ (225 +475)  =  380/ (380 + x + 304)

225 / 700  = 380 / 684 + x

225 * ( 684 + x ) = 700*380

153900 + 225*x = 266000

225*x = 266000 - 153900

225*x = 112100

x = 498,22

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explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer

v = 1/3 a^2h

step-by-step explanation:

the volume is 1/3 a^2h.